find function if:

f(x) +f(1/x)=1&

f(1+2x)=1/2f(x)  where x is positive rational no.

Are you sure there is no other data given??

f(x) = 1- f(1/x)

f(x) = 2 f(1+2x)

so, putting x=1,  f(1) = 1-f(1)

=>f(1) = 1/2.

and, f(1) = 2 f(3)

=>f(3) =1/4.

putting, x=1/2.

f(1/2) = 1-f(2)  and f(1/2) = 2 f(2)

=> f(2) = 1/3.

hence, we can say, f(x) = 1/(1+x)